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calculus, again

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Hey can you help me find the exact value of x in the equation 5^2x=3^(x+1)? Thanks a lot, this website is cool and helpful!

  • calculus, again - ,

    take the log of both sides

    log(5^2x) = log (3^(x+1))
    2xlog5 = (x+1)log3
    2xlog5 = xlog3 + log3
    2xlog5 - xlog3 = log3
    x(2log5 - log3) = log 3
    x = log3/(2log5 - log3)
    x = .5181489...

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